arXiv subjects

Michael J. Landry

Publications and source records attributed to Michael J. Landry.

12 recordsLinked to original sources

arXiv2026

Tensor-Network Finite Elements for Analytic Operator Equations

Operator equations (OEs) underpin quantitative modeling across science and engineering. Finite-element (FE) methods discretize continuous OEs into finite-dimensional algebraic systems, whereas tensor networks (TNs) provide flexible variational representations of correlated discrete systems. Here, we develop a framework that connects FE with TN for analytic OEs. The power of this method comes from its ability to convert highly non-linear partial differential equations into linear matrix equations. In particular, we show that FE discretization induces a hierarchy of multilinear interaction tensors, through which differential, integral, nonlinear, memory, and delay equations can be expressed within a common algebraic structure. The resulting systems are reformulated as weighted-residual optimization problems over TN degrees of freedom. Matrix-product-state calculations for one-dimensional linear and nonlinear diffusion reproduce conventional solutions with controlled error while preserving continuity and Neumann boundary conditions. The framework provides a common variational language for analytic OEs and establishes a direct connection between FE numerical formalism and TN variational algorithms, offering a general foundation for TN-based and quantum-inspired approaches to solving OEs.

math.NA↗

arXiv2026

Quantum Theory of Functionally Graded Materials

Functionally graded materials (FGMs) are composites whose composition or microstructure varies continuously in space, producing position-dependent mechanical and functional properties. In recent years, FGMs have gained significant attention due to advances in additive manufacturing, which enable precise spatial control of composition and orientation. However, their graded, aperiodic structure breaks the assumptions of Bloch's theorem, making first-principles electronic and electromagnetic calculations challenging. Here we develop an ab initio quantum theoretical framework for the electromagnetic properties of FGMs. Using a non-interacting electron model, we formulate a theory of modulated Bloch states, derive effective field equations, and solve them by proposing a generalized WKB (GWKB) method, an effective mass approximation, the Boltzmann equation, and numerical approaches. Our GWKB solution is not semiclassical but remains valid in the fully quantum regime. We show that effective observables such as conductivity, magnetic permeability, and electric permittivity generally do not admit a tensorial description in graded media, and that engineered orientational gradients enable precise control of Landau quantization. As a device example, we further develop a theory of graded p-n junctions with enhanced electronic tunability. This framework lays the quantum foundation for predictive design of graded composite materials, enabling AI-accelerated discovery of next-generation functional architectures.

cond-mat.mtrl-sci↗

arXiv2025

Theory of the Photomolecular Effect

It is well-known that water in both liquid and vapor phases exhibits exceptionally weak absorption of light in the visible range. Recent experiments, however, have demonstrated that at the liquid-air interface, absorption in the visible range is drastically increased. This increased absorption results in a rate of evaporation that exceeds the theoretical thermal limit by between two and five times. Curiously, the evaporation rate peaks at green wavelengths of light, while no corresponding absorptance peak has been observed. Experiments suggest that photons can cleave off clusters of water molecules at the surface, but no clear theoretical model has yet been proposed to explain how this is possible. This paper aims to present such a model and explain this surprising and important phenomenon.

cond-mat.soft↗

arXiv2023

Active actions: effective field theory for active nematics

Active matter consumes energy from the environment and transforms it into mechanical work. Notable examples from biology include cell division, bacterial swarms, and muscle contraction. In this work, we investigate the nature of active matter systems using the powerful effective field theory toolbox. This allows us to construct the most general theory without ambiguity up to a given order in the derivative expansion. Our primary focus is active nematics -- liquid crystal systems that spontaneously break rotational but not translational symmetry -- in two spatial dimensions. (Such spontaneous symmetry breaking is allowed if the nematic is embedded in a higher dimensional space.) While we focus on this one particular class of physical system, the tools developed here can in principle be applied to any active matter system. Our theories give unambiguous predictions for the relationship between fluctuations and equations of motion in the presence of activity, generalizing the standard fluctuation-dissipation relations characteristic of passive systems.

cond-mat.soft↗

arXiv2023

Apparently superluminal superfluids

We consider the superfluid phase of a specific renormalizable relativistic quantum field theory. We prove that, within the regime of validity of perturbation theory and of the superfluid effective theory, there are consistent and regular vortex solutions where the superfluid's velocity field as traditionally defined smoothly interpolates between zero and arbitrarily large superluminal values. We show that this solution is free of instabilities and of superluminal excitations. We show that, in contrast, a generic vortex solution for an ordinary fluid does develop an instability if the velocity field becomes superluminal. All this questions the characterization of a superfluid velocity field as the actual velocity of ``something".

hep-th↗

arXiv2023

A systematic formulation of chiral anomalous magnetohydrodynamics

We present a new way of deriving effective theories of dynamical electromagnetic fields in general media. It can be used to give a systematic formulation of magnetohydrodynamics (MHD) with strong magnetic fields, including systems with chiral matter and Adler-Bell-Jackiw (ABJ) anomaly. We work in the regime in which velocity and temperature fluctuations can be neglected. The resulting chiral anomalous MHD incorporates and generalizes the chiral magnetic effect, the chiral separation effect, the chiral electric separation effect, as well as recently derived strong-field MHD, all in a single coherent framework. At linearized level, the theory predicts that the chiral magnetic wave does not survive dynamical electromagnetic fields. A different chiral wave, to which we refer as the chiral magnetic electric separation wave, emerges as a result of dynamical versions of the chiral electric separation effect and the chiral magnetic effect. We predict its wave velocity. We also introduce a simple, but solvable nonlinear model to explore the fate of the chiral instability.

hep-ph↗

arXiv2022

Higher-form and (non-)Stückelberg symmetries in non-equilibrium systems

We investigate the role of higher-form symmetries in non-equilibrium systems from the perspective of effective actions defined on the Schwinger-Keldysh contour. To aid our investigation, we extend the coset construction to account for $p$-form symmetries at zero and finite temperature. Additionally we investigate how, out of equilibrium, symmetries of the action need not lead to meaningful conserved currents at the level of the equations of motion. For reasons that will become apparent, we term symmetries with conserved currents Stückelberg symmetries and those without meaningful conserved currents non-Stückelberg symmetries (NSS). Ordinarily any action constructed exclusively from building-blocks furnished by the coset construction will have Stückelberg symmetries associated with each symmetry generator. To expand the set of systems describable by the coset construction, we devise a method by which NSS generators can be included as well. While 0-form NSS are quite common in non-equilibrium effective actions, the introduction of $p$-form NSS is novel. We use these $p$-form NSS to investigate spontaneous symmetry breaking of $p$-form symmetries. We find that in non-equilibrium systems, whether or not a symmetry appears spontaneously broken can depend on the time-scale over which the system is observed. Finally, using our new coset construction, we formulate actions for a number of systems including chemically reacting fluids, Yang-Mills theory, Chern-Simons theory, magnetohydrodynamic systems, and dual superfluid and solid theories.

hep-th↗

arXiv2021

Non-equilibrium effective field theory and second sound

We investigate the phenomenon of second sound in various states of matter from the perspective of non-equilibrium effective field theory (EFT). In particular, for each state of matter considered, we find that at least two (though sometimes multiple) qualitatively different EFTs exist at finite temperature such that there is always at least one EFT with a propagating second-sound wave and at least one with no such second-sound wave. To aid in the construction of these EFTs, we use the method of cosets developed for non-equilibrium systems. It turns out that the difference between the EFTs with and without second-sound modes can be understood as arising from different choices of a new kind of inverse Higgs constraint. Finally, we demonstrate that it is possible to bypass the need for new inverse Higgs constraints by formulating EFTs on a new kind of manifold that is like the usual fluid worldvolume, but with reduced gauge symmetries.

hep-th↗

arXiv2020

Vortices and waves in light dark matter

In a galactic halo like the Milky Way, bosonic dark matter particles lighter than about $30$ eV have a de Broglie wavelength larger than the average inter-particle separation and are therefore well described as a set of classical waves. This applies to, for instance, the QCD axion as well as to lighter axion-like particles such as fuzzy dark matter. We show that the interference of waves inside a halo inevitably leads to vortices, locations where chance destructive interference takes the density to zero. The phase of the wavefunction has non-trivial winding around these points. This can be interpreted as a non-zero velocity circulation, so that vortices are sites where the fluid velocity has a non-vanishing curl. Using analytic arguments and numerical simulations, we study the properties of vortices and show they have a number of universal features: (1) In three spatial dimensions, the generic defects take the form of vortex rings. (2) On average there is about one vortex ring per de Broglie volume and (3) generically only single winding ($\pm 1$) vortices are found in a realistic halo. (4) The density near a vortex scales as $r^2$ while the velocity goes as $1/r$, where $r$ is the distance to vortex. (5) A vortex segment moves at a velocity inversely proportional to its curvature scale so that smaller vortex rings move faster, allowing momentary motion exceeding escape velocity. We discuss observational/experimental signatures from vortices and, more broadly, wave interference. In the ultra-light regime, gravitational lensing by interference substructures leads to flux anomalies of $5-10 \%$ in strongly lensed systems. For QCD axions, vortices lead to a diminished signal in some detection experiments but not in others. We advocate the measurement of correlation functions by axion detection experiments as a way to probe and capitalize on the expected interference substructures.

astro-ph.CO↗

arXiv2020

The coset construction for particles of arbitrary spin

When a Poincaré-invariant system spontaneously breaks continuous internal symmetries, Goldstones's theorem demands the existence of massless, spin-zero excitations in a one-to-one correspondence with the broken symmetry generators. When a system spontaneously breaks Poincaré symmetry, however, the kinds of excitations that satisfy Goldstone's theorem can be quite unusual. In particular, they may have any spin and need not be particles or even quasiparticles. The standard coset construction used to formulate effective actions of Goldstones, however, is rather restrictive and is incapable of generating the full spectrum of possibilities allowed by Goldstone's theorem. We propose a (partial) remedy to this problem by postulating a novel coset construction for systems that spontaneously break Poincaré symmetry. This new construction is capable of generating effective actions with a wide range of Goldstone excitations---including fermionic degrees of freedom---even when all symmetries are bosonic. To demonstrate it's utility, we focus on constructing effective actions for point particles of various spins. We recover the known result that a particle of spin $s$ requires an $\mathcal N=2s$ supersymmetric worldline reparameterization gauge symmetry, which we implement at the level of the coset construction. In the process, we discover that massless particles require a novel kind of inverse Higgs constraint that bears some resemblance to the dynamical inverse Higgs constraints that appear in certain fermi liquid effective field theories. We then consider particles that, in addition to quantum spin, have finite spatial extent and are free to rotate. We derive a novel action for such particles and find a `spin-orbital' coupling between the intrinsic quantum spin and the physical-rotation degrees of freedom.

hep-th↗

arXiv2020

The coset construction for non-equilibrium systems

We propose a systematic coset construction of non-equilibrium effective field theories (EFTs) governing the long-distance and late-time dynamics of relativistic, finite-temperature condensed matter systems. Our non-equilibrium coset construction makes significant advances beyond more standard coset constructions in that it takes advantage of recently-developed techniques, which allow the formulation of non-equilibrium effective actions that account for quantum and thermal fluctuations as well as dissipation. Because these systems exist at finite temperature, the EFTs live on the closed-time-path of the Schwinger-Keldysh contour. Since the coset construction and the non-equilibrium effective actions may be unfamiliar to many readers, we include brief introductions to these topics in an effort to make this paper self-contained. To demonstrate the legitimacy of this coset construction, we successfully reproduce the known EFTs for fluids and superfluids at finite temperature. Then, to demonstrate its utility, we construct novel EFTs for solids, supersolids, and four phases of liquid crystals, all at finite temperature. We thereby combine the non-equilibrium effective action and the coset construction to create a powerful tool that can be used to study many-body systems out of thermal equilibrium.

hep-th↗

arXiv2020

Dynamical chemistry: non-equilibrium effective actions for reactive fluids

We present two approaches for describing chemical reactions taking place in fluid phase. The first method mirrors the usual derivation of the hydrodynamic equations of motion by relating conserved---or to account for chemical reactions, non-conserved---currents to local-equilibrium parameters. The second method involves a higher-brow approach in which we attack the same problem from the perspective of non-equilibrium effective field theory (EFT). Non-equilibrium effective actions are defined using the in-in formalism on the Schwinger-Keldysh contour and are therefore capable of describing thermal fluctuations and dissipation as well as quantum effects. The non-equilibrium EFT approach is especially powerful as all terms in the action are fully specified by the symmetries of the system; in particular the second law of thermodynamics does not need to be included by hand, but is instead derived from the action itself. We find that the equations of motion generated by both methods agree, but the EFT approach yields certain advantages. To demonstrate some of these advantages we construct a quadratic action that is valid to very small distance scales---much smaller than the scales at which ordinary hydrodynamic theories break down. Such an action captures the full thermodynamic and quantum behavior of reactions and diffusion at quadratic order. Finally, taking the low-frequency and low-wavenumber limit, we reproduce the linearized version of the well-known reaction-diffusion equations as a final coherence check.

hep-th↗